## Step 1: Define the variables and their corresponding symbolic notation
Let's denote the variables as follows:
- Mbps bandwidth allocated to monitoring: $x_1$
- patches per day: $x_2$
- network administrators: $x_3$
- system administrators: $x_4$
- intrusion analysts: $x_5$
- security engineers: $x_6$

## Step 2: Formulate the objective function
The objective function to minimize is $2x_1 + x_2 + 6x_3 + 9x_4 + 8x_5 + 3x_6$.

## 3: Define the constraints
1. $21x_1 \leq 450$
2. $x_2 \leq 450$
3. $9x_3 \leq 450$
4. $23x_4 \leq 450$
5. $15x_5 \leq 450$
6. $5x_6 \leq 450$
7. $x_2 + 5x_6 \geq 30$
8. $21x_1 + 23x_4 \geq 63$
9. $23x_4 + 5x_6 \geq 63$
10. $x_2 + 9x_3 \geq 50$
11. $21x_1 + x_2 \geq 43$
12. $15x_5 + 5x_6 \geq 52$
13. $9x_3 + 23x_4 \geq 46$
14. $21x_1 + 15x_5 \geq 55$
15. $21x_1 + x_2 + 9x_3 + 23x_4 + 15x_5 + 5x_6 \geq 55$
16. $-3x_3 + 3x_6 \geq 0$
17. $x_2 + 9x_3 \leq 354$
18. $21x_1 + x_2 \leq 299$
19. $x_2 + 5x_6 \leq 410$
20. $21x_1 + 15x_5 \leq 379$
21. $21x_1 + 15x_5 + 5x_6 \leq 265$
22. $9x_3 + 15x_5 + 5x_6 \leq 143$
23. $21x_1 + x_2 + 23x_4 \leq 272$
24. $x_2 + 23x_4 + 15x_5 \leq 352$
25. $21x_1 + 23x_4 + 15x_5 \leq 144$
26. $9x_3 + 23x_4 + 15x_5 \leq 247$

## 4: Symbolic Representation
```json
{
    'sym_variables': [
        ('x1', 'Mbps bandwidth allocated to monitoring'), 
        ('x2', 'patches per day'), 
        ('x3', 'network administrators'), 
        ('x4', 'system administrators'), 
        ('x5', 'intrusion analysts'), 
        ('x6', 'security engineers')
    ], 
    'objective_function': '2*x1 + x2 + 6*x3 + 9*x4 + 8*x5 + 3*x6', 
    'constraints': [
        '21*x1 <= 450',
        'x2 <= 450',
        '9*x3 <= 450',
        '23*x4 <= 450',
        '15*x5 <= 450',
        '5*x6 <= 450',
        'x2 + 5*x6 >= 30',
        '21*x1 + 23*x4 >= 63',
        '23*x4 + 5*x6 >= 63',
        'x2 + 9*x3 >= 50',
        '21*x1 + x2 >= 43',
        '15*x5 + 5*x6 >= 52',
        '9*x3 + 23*x4 >= 46',
        '21*x1 + 15*x5 >= 55',
        '21*x1 + x2 + 9*x3 + 23*x4 + 15*x5 + 5*x6 >= 55',
        '-3*x3 + 3*x6 >= 0',
        'x2 + 9*x3 <= 354',
        '21*x1 + x2 <= 299',
        'x2 + 5*x6 <= 410',
        '21*x1 + 15*x5 <= 379',
        '21*x1 + 15*x5 + 5*x6 <= 265',
        '9*x3 + 15*x5 + 5*x6 <= 143',
        '21*x1 + x2 + 23*x4 <= 272',
        'x2 + 23*x4 + 15*x5 <= 352',
        '21*x1 + 23*x4 + 15*x5 <= 144',
        '9*x3 + 23*x4 + 15*x5 <= 247'
    ]
}
```

## 5: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="Mbps bandwidth allocated to monitoring", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="patches per day", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="network administrators", vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name="system administrators", vtype=gurobi.GRB.INTEGER)
    x5 = model.addVar(name="intrusion analysts", vtype=gurobi.GRB.INTEGER)
    x6 = model.addVar(name="security engineers", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(2*x1 + x2 + 6*x3 + 9*x4 + 8*x5 + 3*x6, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(21*x1 <= 450)
    model.addConstr(x2 <= 450)
    model.addConstr(9*x3 <= 450)
    model.addConstr(23*x4 <= 450)
    model.addConstr(15*x5 <= 450)
    model.addConstr(5*x6 <= 450)
    model.addConstr(x2 + 5*x6 >= 30)
    model.addConstr(21*x1 + 23*x4 >= 63)
    model.addConstr(23*x4 + 5*x6 >= 63)
    model.addConstr(x2 + 9*x3 >= 50)
    model.addConstr(21*x1 + x2 >= 43)
    model.addConstr(15*x5 + 5*x6 >= 52)
    model.addConstr(9*x3 + 23*x4 >= 46)
    model.addConstr(21*x1 + 15*x5 >= 55)
    model.addConstr(21*x1 + x2 + 9*x3 + 23*x4 + 15*x5 + 5*x6 >= 55)
    model.addConstr(-3*x3 + 3*x6 >= 0)
    model.addConstr(x2 + 9*x3 <= 354)
    model.addConstr(21*x1 + x2 <= 299)
    model.addConstr(x2 + 5*x6 <= 410)
    model.addConstr(21*x1 + 15*x5 <= 379)
    model.addConstr(21*x1 + 15*x5 + 5*x6 <= 265)
    model.addConstr(9*x3 + 15*x5 + 5*x6 <= 143)
    model.addConstr(21*x1 + x2 + 23*x4 <= 272)
    model.addConstr(x2 + 23*x4 + 15*x5 <= 352)
    model.addConstr(21*x1 + 23*x4 + 15*x5 <= 144)
    model.addConstr(9*x3 + 23*x4 + 15*x5 <= 247)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Mbps bandwidth allocated to monitoring: ", x1.varValue)
        print("patches per day: ", x2.varValue)
        print("network administrators: ", x3.varValue)
        print("system administrators: ", x4.varValue)
        print("intrusion analysts: ", x5.varValue)
        print("security engineers: ", x6.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```